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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>First, we consider a particular example.</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation}
y^{\prime \prime}-y=0.\tag{3.1.4}
\end{equation}
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<p class="continuation">Inspect: <span class="process-math">\(y^{\prime \prime}=y\)</span> and note that <span class="process-math">\(((e)^x)^{\prime}=e^x\text{,}\)</span> <span class="process-math">\((e^x)^{\prime \prime}=e^x\text{.}\)</span> Thus, <span class="process-math">\(y_1(x)=e^x\)</span> is a solution. Also, <span class="process-math">\((e^{-x})^{\prime \prime}=e^{-x}\text{.}\)</span> Thus, <span class="process-math">\(y_2(x)=e^{-x}\)</span> is another solution. Further, <span class="process-math">\(C_1 e^x\)</span> and <span class="process-math">\(C_2 e^{-x}\)</span> (<span class="process-math">\(C_1\)</span> and <span class="process-math">\(C_2\)</span> are any constants) are still two solutions. Also,</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
(C_1 e^x+C_2 e^{-x})^{\prime \prime}=C_1 e^x+C_2 e^{-x}.
\end{equation*}
</div>
<p class="continuation">Thus, <span class="process-math">\(C_1 e^x+C_2 e^{-x}\)</span> is also the solution, representing double infinite family of solutions, see Figure <code class="code-inline tex2jax_ignore">[cross-reference to target(s) "fig3" missing or not unique]</code>.</p>
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